Question: The measures of a pair of supplementary angles are in the ratio of 7:2. How many degrees are in the measure of their positive difference?
Answer: Since the measures are in the ratio $7:2$, the measures are $7x$ and $2x$ for some value of $x$.  Since the angles are supplementary, we have $7x + 2x = 180^\circ$, so $9x = 180^\circ$ and $x= 20^\circ$.  Therefore, the angle measures are $7x=140^\circ$ and $2x=40^\circ$, so their positive difference is $140^\circ - 40^\circ = \boxed{100^\circ}$.